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Graphing Quadratic Functions: Vertex Form Method

Learn how to find the vertex of a quadratic function using the vertex formula. Step-by-step examples with x and y-coordinate calculations. Understand how to graph by utilizing the Vertex Formula effectively.

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Graphing Quadratic Functions: Vertex Form Method

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  1. Section 7.2 Graphing Quadratic Functions in Standard From

  2. Process To find the vertex of the graph of a quadratic function Find the x-coordinate of the vertex by using the vertex formula 2. Find the y-coordinate of the vertex by evaluating f at the value found in step 1. That is, find − b 2a . Section 7.2 Slide 2 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Vertex Formula

  3. Example Find the vertex of the graph of a = 1, b = –4, and c = 7 Find the x-coordinate by substituting a and b into the formula Find the y-coordinate by finding f (2): So, the vertex is (2, 3) Solution Section 7.2 Slide 3 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Find the Vertex

  4. Example Sketch a graph of a = 2, b = 10, and c = 7 Find the x-coordinate of the vertex: Find the y-coordinate of the vertex: So, the vertex is (–2.5, –5.5) Find additional input-output pairs: Solution Section 7.2 Slide 4 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function

  5. Example Solution Continued Section 7.2 Slide 5 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function

  6. Example Sketch a graph of a = –2.2, b = 6.1, and c = 1.4 Find the x-coordinate of the vertex: Find the y-coordinate of the vertex: So, the vertex is (1.39, 5.63) Find additional input-output pairs: Solution Section 7.2 Slide 6 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function

  7. Example Solution Continued Section 7.2 Slide 7 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function

  8. Property For a quadratic function whose graph has vertex (h, k), If a < 0, then the parabola opens downward and the maximum value of the function is k • If a > 0, then the parabola opens upward and the minimum value of the function is k Section 7.2 Slide 8 Minimum of Maximum Value Maximum of Minimum Value of a Function

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